Question Number 143709 by mnjuly1970 last updated on 17/Jun/21 Commented by mnjuly1970 last updated on 17/Jun/21 $$\:\:\:\:{P}\:{rove}\:::\Uparrow\Uparrow\Uparrow \\ $$ Commented by TheHoneyCat last updated on…
Question Number 143708 by ZiYangLee last updated on 17/Jun/21 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{3}}{\mathrm{4}^{} }+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{3}^{\mathrm{3}} }{\mathrm{4}^{\mathrm{3}} }+\frac{\mathrm{3}^{\mathrm{4}} }{\mathrm{4}^{\mathrm{4}} }+\frac{\mathrm{3}^{\mathrm{5}} }{\mathrm{4}^{\mathrm{5}} }+\ldots=\mathrm{3} \\ $$ Answered by…
Question Number 12635 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 27/Apr/17 Answered by mrW1 last updated on 27/Apr/17 $${x}^{\mathrm{2}} −\mathrm{2}{x}\mathrm{tan}\:\varphi−\mathrm{1} \\ $$$$={x}^{\mathrm{2}} −\mathrm{2}{x}\mathrm{tan}\:\varphi+\mathrm{tan}^{\mathrm{2}} \:\varphi−\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\varphi \\ $$$$=\left({x}−\mathrm{tan}\:\varphi\right)^{\mathrm{2}}…
Question Number 78168 by TawaTawa last updated on 14/Jan/20 $$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x},\:\mathrm{y},\:\mathrm{z}\:\:\mathrm{if}:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:\:=\:\:\mathrm{42} \\ $$ Commented by MJS last updated on 15/Jan/20 $${x}\in\mathbb{N},\:\mathbb{Z},\:\mathbb{R}? \\ $$…
Question Number 143706 by Huy last updated on 17/Jun/21 $$\mathrm{2}^{\mathrm{x}} +\mathrm{9}^{\mathrm{y}} =\mathrm{x}^{\mathrm{2}} +\mathrm{9xy}+\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{Find}\:\mathrm{x},\mathrm{y}\in\mathbb{N} \\ $$ Answered by TheHoneyCat last updated on 17/Jun/21 $$…
Question Number 12632 by @ANTARES_VY last updated on 27/Apr/17 $$\boldsymbol{\mathrm{y}}=\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{9}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{5}}\:\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{values}}\:\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{feture}}\:\:\boldsymbol{\mathrm{set}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{prime}}\:\:\boldsymbol{\mathrm{numbers}}? \\ $$ Answered by abcd last updated on 27/Apr/17 Commented by…
Question Number 143701 by help last updated on 17/Jun/21 Commented by Eric002 last updated on 17/Jun/21 $${can}\:{you}\:{put}\:{a}\:{better}\:{picture}\: \\ $$ Answered by TheHoneyCat last updated on…
Question Number 12631 by 786786AM last updated on 27/Apr/17 $$\:\:\mathrm{Find}\:\mathrm{tbe}\:\mathrm{sloution}\:\mathrm{set}\:\mathrm{of}\:\frac{\mathrm{5}}{\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{3}+\mathrm{x}\right)}\:>\:\mathrm{0}. \\ $$ Answered by mrW1 last updated on 27/Apr/17 $$\left({x}−\mathrm{3}\right)\left({x}+\mathrm{3}\right)>\mathrm{0} \\ $$$${x}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} >\mathrm{0} \\…
Question Number 12630 by sin (x) last updated on 27/Apr/17 $${f}\left({x}\right)=\left({x}^{} −\mathrm{3}\right)^{\mathrm{10}} \\ $$$$ \\ $$$$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left(\mathrm{2}+\mathrm{5}{h}\right)−{f}\left(\mathrm{2}+\mathrm{3}{h}\right)}{{h}}=? \\ $$ Answered by ajfour last updated on…
Question Number 143702 by henderson last updated on 17/Jun/21 $${n}\:\in\:\mathrm{IN}. \\ $$$${I}_{{n}} \:=\:\int_{\mathrm{1}} ^{\:\mathrm{e}} {x}^{{n}+\mathrm{1}} {lnx}\:{dx}. \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\left(\boldsymbol{{I}}_{\boldsymbol{{n}}} \right)\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{increasing}}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{part}}−\boldsymbol{\mathrm{by}}−\boldsymbol{\mathrm{part}}\:\boldsymbol{\mathrm{integration}},\:\boldsymbol{\mathrm{calculate}}\:\boldsymbol{{I}}_{\boldsymbol{{n}}} . \\ $$ Answered…